In the investigation of disease dynamics, the effect of covariates on the hazard function is a major\ntopic. Some recent smoothed estimation methods have been proposed, both frequentist and Bayesian,\nbased on the relationship between penalized splines and mixed models theory. These approaches\nare also motivated by the possibility of using automatic procedures for determining the\noptimal amount of smoothing. However, estimation algorithms involve an analytically intractable\nhazard function, and thus require ad-hoc software routines. We propose a more user-friendly alternative,\nconsisting in regularized estimation of piecewise exponential models by Bayesian\nP-splines. A further facilitation is that widespread Bayesian software, such as WinBUGS, can be\nused. The aim is assessing the robustness of this approach with respect to different prior functions\nand penalties. A large dataset from breast cancer patients, where results from validated clinical\nstudies are available, is used as a benchmark to evaluate the reliability of the estimates. A second\ndataset from a small case series of sarcoma patients is used for evaluating the performances of the\nPE model as a tool for exploratory analysis. Concerning breast cancer data, the estimates are robust\nwith respect to priors and penalties, and consistent with clinical knowledge. Concerning soft\ntissue sarcoma data, the estimates of the hazard function are sensitive with respect to the prior for\nthe smoothing parameter, whereas the estimates of regression coefficients are robust. In conclusion,\nGibbs sampling results an efficient computational strategy. The issue of the sensitivity with\nrespect to the priors concerns only the estimates of the hazard function, and seems more likely to occur when non-large case series are investigated, calling for tailored solutions.
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